Parameter Estimation

• Bernard Flury
Part of the Springer Texts in Statistics book series (STS)

Abstract

Estimation of parameters is a central topic in statistics. In probability theory we study the distribution of random variables, assuming they follow certain distributions, and try to find out what is likely to happen and what is unlikely. Conversely, in statistics we observe data and try to find out which distribution generated the data. In the words of my colleague R.B. Fisher: “In probability, God gives us the parameters and we figure out what is going to happen. In statistics, things have already happened, and we are trying to figure out how God set the parameters.”

Keywords

Mean Square Error Likelihood Function Maximum Likelihood Estimator Bootstrap Sample Wing Length
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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1. Casella, G., and Berger, R.L. 1990. Statistical Inference. Belmont, CA: Duxbury Press.
2. Silvey, S.D. 1975. Statistical Inference. London: Chapman and Hall.
3. Diaconis, P., and Efron, B. 1983. Computer-intensive methods in statistics. Scientific American 248 (May), 116–130.
4. Efron, B. 1982. The Jackknife, the Bootstrap, and Other Resampling Plans. Philadelphia: Society for Industrial and Applied Mathematics.
5. Efron, B., and Gong, G. 1983. A leisurely look at the bootstrap, the jackknife, and other resampling plans. The American Statistician 37, 36–48.
6. Efron, B., and Tibshirani, R. 1993. An Introduction to the Bootstrap. London: Chapman and Hall.
7. Edwards, A.W.F. 1984 Likelihood Cambridge University Press Cambridge
8. Kalbfleisch, J.G. 1985 Probability and Statistical Inference 2 Springer New YorkGoogle Scholar
9. Watson, G.S. 1964. A note on maximum likelihood. Sankhya A 26, 303–304.
10. Dempster, A.P., Laird, N.M., and Rubin, D.B. 1977. Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society Series B, 39, 1–38.
11. Little, R.J.A., and Rubin, D.B. 1987. Statistical Analysis with Missing Data. New York: Wiley.
12. McLachlan, G.J., and Krishnan, T. 1997. The EM Algorithm and Extensions. New York: Wiley.
13. Rubin, D.B., and Szatrowski, T.H. 1982. Finding maximum likelihood estimates of patterned covariance matrices by the EM algorithm. Biometrika 69, 657–660.